Question

Find the order and degree of the differential equation ${\left[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)\right]}^{\frac{3}{4}}=\frac{d^{2}y}{d{x}^2}$

• A. order=2
  degree=3
• B. order=2
  degree=4
• C. order=2
  degree=$\frac{3}{4}$
• D. order=2
  degree= not defined

Answer 1

Answer: (D)

We have, ${\left[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)\right]}^{3/4}=\frac{d^{2}y}{d{x}^2}$
$\Rightarrow {\left(\frac{d^{2}y}{d{x}^2}\right)}^4={\left[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)\right]}^8$
Clearly, order $=2$ and degree $=$ not defined